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The problem asks to find the correct form of a triple integral, where the order of integration is first with respect to \( z \), then \( x \), and finally \( y \). The rectangular box is given as:

\[
B = [a, b] \times [c, d] \times [r, s]
\]

### Translation:
- \( [a, b] \) refers to the limits for \( x \),
- \( [c, d] \) refers to the limits for \( y \),
- \( [r, s] \) refers to the limits for \( z \).

### The triple integral:

Given that the order of integration is \( z \) first, then \( x \), and finally \( y \), the integral should be structured as follows:

\[
\int_{c}^{d} \left( \int_{a}^{b} \left( \int_{r}^{s} f(x, y, z) \, dz \right) dx \right) dy
\]

This matches the order specified: \( z \to x \to y \).

Would you like further details on how this setup works, or do you have specific questions? Here are some relative questions for further exploration:

1. What is the significance of changing the order of integration in triple integrals?
2. How do limits of integration change when dealing with different regions (e.g., non-rectangular boxes)?
3. What conditions must be met for switching the order of integration in multiple integrals?
4. Can you explain the geometric interpretation of integrating first with respect to \( z \)?
5. How would this integral change if the limits of integration were functions instead of constants?

**Tip:** Always ensure the region of integration matches the order in which the variables are integrated when setting up multiple integrals.

Se f é contínua em uma caixa retangular B = [a, b] × [c, d] × [r, s], escolha a alternativa que contenha a integral tripla que será integrada primeiro em relação à z, depois em relação à x, e, finalmente, em relação à y.

This problem requires finding the correct form of a triple integral with the specified order of integration: first with respect to z, then x, and finally y, within the limits of a rectangular box defined by [a, b] × [c, d] × [r, s]. Learn about the triple integral setup and the application of multivariable calculus.

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